1. Business Finance
Michael Dimond

2. Ordinary Annuity: FV & PV
A stream of cash flows where all payments are equal is called an Annuity.
In an Ordinary Annuity, each payment happens at the end of the period.
Your financial calculator can solve these easily and quickly.
Find PV given n, i, and PMT
Find FV given n, i, and PMT
For the magic machine, the inputs would be:
PV = ? (This is what we’re solving for)
n = 60 (monthly payments)
i = 12/12 (12% ÷ 12 months)
PMT = 100 (per month)
FV = 0 (This has no value once the final payment is delivered)
Notice that these three items must always be in the same timeframe: monthly annually, daily… whatever is in the scenario

3. About loans
To correctly analyze a loan scenario, draw a timeline showing when payments happen, and for what amount.
Amortized loans are annuities
Consider the example of a mortgage: Each payment is the same until the loan is paid off.
Simple interest loans are not annuities. The principal does not change if each payment is interest only.

4. Ordinary Annuity with an additional payout
What happens if there is a stream of payments, and also a lump sum being paid at the end of the timeline?
Timeline…
Find PV given n, i, PMT & FV

5. Comments about Annuity Due
An Annuity Due has payments which happen at the beginning of each period instead of the end.
Typically used in real estate…
Timelines…
Difference in value…
Calculator setting…
Ordinary Annuity
Annuity Due
i = 12%
i = 12% 1 2 3 1 2 3
100
100
100
100
100
100
100 ÷ (1+0.12)1
100 ÷ (1+0.12)1
100 ÷ (1+0.12)2
100 ÷ (1+0.12)2
100 ÷ (1+0.12)3

7. Discounting unequal cash flows
If you require a 12% annual return, what would you pay for…
…$90 to be delivered in 1 year? ($ )
…$95 to be delivered in 2 years? ($ )
…$99 to be delivered in 3 years? ($ )
…all of the above?
By adding together the present values, you find the value of all the cash flows in the stream.
i = 12% 1 2 3 ? 90 95 99
90 ÷ (1+0.12)1
There’s an easier way… kind of.
95 ÷ (1+0.12)2
99 ÷ (1+0.12)3

8. Using the calculator (NPV function)

9. Using the calculator (NPV function)